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Re: [Axiom-developer] about Expression Integer

From: Francois Maltey
Subject: Re: [Axiom-developer] about Expression Integer
Date: 20 Feb 2006 10:52:31 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

"Bill Page" <address@hidden> propose :

> There may be some situations, such as in the Axiom interpreter
> where you might wish to warn the user about the sometimes
> unexpected consequences of domains that allow this.

I agree with this, 

For students and I a lot of problems are about :
<< You think that 2 objects are identical if their writing are identical. >>

The 2 way to read the x is logical when we think as axiom, 
but is a trap for students who use computer algebra for solving 
a mathematical exercice.

> But really it is very simple and easy to predict. The problem
> is that most people focus is on the wrong thing. This is especially
> natural if they have previous experience with other computer algebra
> systems.

But almost all my student use derive or maple or a TI-9? for little
computation, and during their mathematical studies they don't learn 
object programming. So it's impossible to say : 
<< learn axiom from the emptyset. >>

I like mupad because easy computation was easy to type, 
but difficult idea can be done with clever idea about Domains.
I hope that axiom should have the same point of view. 

I don't like maple which have very often wrong results because it's impossible
to have type : In maple the fact that 0.0 = 0 gives very surprising result.
So I prefer explain mupad that axiom to my student, because if I don't
have this error I can do a more difficult exercice.

> I could imagine that some innocent looking
> computation would not be correct in the situation above. 

As Martin I already imagine this error :

P := DMP ([x,y], EXPR INT) 
a :P := x 
b := a/x 

differentiate(b,x)                    -- 1/x
differentiate(b+x,x)@EXPR INT         -- 0

I find it's a wonderful idea ((***)) to have an error or a warning during
b := a/x. It's really possible ?
Bill, I don't want to change all the axiom language ;-)
it's the _only_ trap I see in the interpeter.

The other computation are logical for students in mathematics. ;-)
And if a student can understand the coefficient function, he can understand
why it's a silly computation to type monomial (x, [0,0]...)
Bill you think it's must remain possible, why not. 

Have a good day !


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